Course

CAREER: Supporting Students' Proof Practices Through Quantitative Reasoning in Algebra

The aim of this project is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.

Award Number: 
1743356
Funding Period: 
Mon, 03/15/2010 to Fri, 06/30/2017
Full Description: 

The aim of this CAREER project led by Amy Ellis at the University of Wisconsin is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.

Work of the project will produce: (a) insights into ways of unifying two previously disconnected lines of research on quantitative reasoning and proof; (b) models describing realistic ways to support development of students' proof competencies through quantitative reasoning; (c) improvement in students' understanding of algebra through engagement in proof practices based on quantitative reasoning; (d) insights into middle-school students' thinking as they negotiate the transition from elementary to more advanced mathematics; and (e) increased understanding of teachers' knowledge about proof and their classroom practices aimed at helping students progress towards understanding and skill in proof.

This project was previously funded under award #0952415.

Iterative Model Building (IMB): A Program for Training Quality Teachers and Measuring Teacher Quality

This project aims to improve professional development programs for pre-service teachers (PSTs) as a way to improve student learning in mathematics and science. PSTs engage in a series of teaching cycles, and then engage in lesson study groups to develop, teach, and analyze a whole-class lesson. The cycle is completed by reexamining students' knowledge in teaching experiments with pairs of students. These teaching cycles are called Iterative Model Building (IMB).

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0732143
Funding Period: 
Wed, 08/15/2007 to Tue, 07/31/2012
Project Evaluator: 
Center for Evaluation and Education Policy

Biocomplexity and the Habitable Planet -- An Innovative Capstone Course for High School (Collaborative Research: Puttick)

This project is developing a set of instructional materials that engages students and teachers in the science of coupled natural human (CNH) systems. Teacher guides, a website and multimedia resources accompany the four student modules (which focus on an urban watershed, an urban/agricultural system, Amazonia and a polar system).

Award Number: 
0628171
Funding Period: 
Sun, 10/01/2006 to Sun, 03/31/2013
Project Evaluator: 
EDC
Full Description: 

Biocomplexity — A frontier of modern science

The science disciplines that try to understand how biological and earth systems work arose in previous centuries when places that humans had not affected still remained. But in the past century, scientists have begun to realize that to really understand the world we inhabit — how it works, and how it’s changing — we have to accept Homo sapiens as an essential player, and not an intruder. This kind of thinking, which links biology, ecology, physics, chemistry, with human society and behavior, is leading to some very exciting, and sometimes surprising, science.

One term for this emerging science is biocomplexity. Biocomplexity is an umbrella science that integrates the core concepts of ecology, biogeography, ecosystem services, and landscape ecology to understand “coupled human-natural systems” and to identify more effective solutions to the challenges we face in the biosphere.

This course is designed to help students acquire a “biocomplex” way of thinking, by looking at several real situations, some familiar, and some unfamiliar, in which humans are involved as the world changes. Our mission is to foster the understanding of the complex fabric of relationships between humans and the environment, vital and important knowledge for all citizens in an era of global human impact on the environment. We can no longer study “natural” systems without considering human interactions. High school science materials should reflect this critically important fact, and also support students to engage in authentic investigations.

The curriculum uses a case study approach to engage students with biocomplexity in urban, agricultural, tropical and polar systems, in which students address environmental land and resource use challenges increasingly confronted by society. Students engage in inquiry-based investigations, gather data from primary sources, and construct evidence-based arguments. The curriculum is enlivened by multimedia resources, including video, animations, podcasts and slideshows.  The four units each take 7-9 weeks to complete.

Unit One: Urban Biocomplexity : Students develop an understanding of systems thinking at the local scale of their familiarschoolyard ecosystem. They make a land use decision regarding the addition of anathletic field to the school grounds and investigate how land use impacts hydrology,nitrogen flux, biotic factors, social factors, and ecosystem services.

Unit Two: Sprawl and Biocomplexity: Students explore the impact of habitat fragmentation as they consider the proposedconversion of farmland to a suburban housing development. They map landscapeelements and investigate biodiversity, social factors, fluxes of carbon, the economics androle of commodity subsidies, and the impact of “green” design. They debate land usealternatives that include sustainable practices, and build a coherent scientific case to support their land use choice.

Unit Three: Amazonia and Biocomplexity: Students explore connections between the agricultural and grazing practicescurrently responsible for large-scale deforestation in Amazonia and the connections ofdeforestation to local, regional, and global climate. They investigate the role of rainforestin regulating atmospheric gases and stabilizing rainfall. They analyze patterns ofAmazonian deforestation and habitat fragmentation, analyze the economic ecology ofsoybean production, cattle ranching and forestry land uses, and conduct a stakeholderanalysis. Finally, student teams prepare a plan for land in a region in Amazonia, jugglingtypes of land use to optimize other critical factors such as conservation, carbonsequestration, economic benefits and viable agriculture. 

Unit Four: Arctic Biocomplexity: Many arctic species are showing signs of rapid impacts from habitat disruption due to climate change. Students explore these impacts, investigate the flux of heat energy, and learn about population dynamics, conservation biology, adaptation and natural selection to be able to forecast what is likely to happen to selected Arctic species as the climate changes. They construct a case to support recommended conservation strategies.

 

 

Dynamic Geometry in Classrooms

This project is conducting repeated randomized control trials of an approach to high school geometry that utilizes Dynamic Geometry (DG) software and supporting instructional materials to supplement ordinary instructional practices. It compares effects of that intervention with standard instruction that does not make use of computer drawing tools.

Project Email: 
Lead Organization(s): 
Award Number: 
0918744
Funding Period: 
Tue, 09/01/2009 to Sat, 08/31/2013
Project Evaluator: 
Ed Dickey
Full Description: 

The project is conducting repeated randomized control trials of an approach to high school geometry that utilizes dynamic geometry (DG) software and supporting instructional materials to supplement ordinary instructional practices.  It compares effects of that intervention with standard instruction that does not make use of computer drawing/exploraction tools. The basic hypothesis of the study is that use of DG software to engage students in constructing mathematical ideas through experimentation, observation, data recording, conjecturing, conjecture testing, and proof results in better geometry learning for most students. The study tests that hypothesis by assessing student learning in 76 classrooms randomly assigned to treatment and control groups. Student learning is assessed by a geometry standardized test, a conjecturing-proving test, and a measure of student beliefs about the nature of geometry and mathematics in general. Teachers in both treatment and control groups receive relevant professional development, and they are provided with supplementary resource materials for teaching geometry. Fidelity of implementation for the experimental treatment is monitored carefully. Data for answering the several research questions of the study are analyzed by appropriate HLM methods. Results will provide evidence about the effectiveness of DG approach in high school teaching, evidence that can inform school decisions about innovation in that core high school mathematics course. The main research question of the project is: Is the dynamic geometry approach better than the business-as-usual approach in facilitating the geometric learning of our students (and more specifically our economically disadvantaged students) over the course of a full school year?

The main resources/products include geometry teachers’ professional development training materials, suggested dynamic geometry instructional activities to supplement current high school geometry curriculum, instruments such as Conjecturing-Proving Test, Geometry Belief Instrument, Classroom Observation Protocols, DG Implementation Questionnaire and Student Interview Protocols. 

The general plan for the four-year project is as follows:

Year 1: Preparation (All research instruments, professional development training and resource materials, recruitment and training of participants, etc.); 

Year 2: The first implementation of the dynamic geometry treatment, and related data collection and initial data analysis; 

Year 3: The second implementation of the DG treatment, and related data collection and data analysis; 

Year 4: Careful and detailed data analysis and reporting.

We are now in project year 3. Data are collected for the second implementation of the DG treatment. For data collected during project year 2, some initial analysis (the analysis on the geometry pretest and posttest data and the psychometric analysis on the project developed instruments) has been conducted. More thorough analysis of the collected data is still on going. The analysis on the geometry test shows that the experimental group significantly outperformed the control group on geometry performance.

The evaluation will be implemented throughout the project’s four-year duration, with an evolving balance of formative and summative evaluation activities.  In the project’s first three years, the evaluation will emphasize formative functions, designed to inform the project research team of the relative strengths and weaknesses of the research design and execution, and target corrections and improvements of the research components. Summative evaluation activities will also take place in these years with the collection of data on student achievement and teacher change. Evaluation activities for year 4 will focus on the summative evaluation of the project’s accomplishment and especially its impact on participating teachers and students. Evaluation reports will be issued annually with a final summative report presented at the end of year 4.

The research results will be disseminated via the following efforts: 1) Creating and constantly updating the project web site; 2) Publishing the related research articles in research journals such as Journal for Research in Mathematics Education; 3) Presenting at state, regional, national, and international research and professional meetings; 4) Meeting with state and local education agencies, schools, and mathematics teacher educators at other universities for presenting the research findings and using the DG approach in more schools and more mathematics teacher education programs; and 5) Contacting more school districts, with a view to developing relationships and ties that would smooth the way to disseminate the research results.

Current Climate Changes over Eastern Siberia and Interior Alaska and their Impact on Permafrost Landscapes, Ecosystem Dynamics, and Hydrological Regime

Through integration of research and education, this project is providing high resolution data on the spatial distribution of the thermal state of permafrost in Alaska, improving the general knowledge of Earth's climatic patterns, bringing science to remote Alaskan villages, and providing an opportunity for younger generations to take part in understanding Earth's climatic and hydrologic systems.

Partner Organization(s): 
Award Number: 
0731739
Funding Period: 
Thu, 05/15/2008 to Sat, 04/30/2011

CEIN: Predictive Toxicology Assessment and Safe Implementation of Nanotechnology in the Environment

This project establishes a Center to conduct research and education on the interactions of nanomaterials with living systems and with the abiotic environment. The research combines high throughput screening assays with computational and physiological modeling to predict impacts at higher levels of biological organization. It will unite the fields of engineering, chemistry, physics, materials science, cell biology, ecology, toxicology, computer modeling, and risk assessment to establish the foundations of a new scientific discipline: environmental nanotoxicology.

Award Number: 
0830117
Funding Period: 
Mon, 09/01/2008 to Sat, 08/31/2013

Researching the Expansion of K-5 Mathematics Specialist Program into Rural School Systems

This project addresses the challenge “How can promising innovations be successfully implemented, sustained, and scaled in schools and districts in a cost effective manner?” Project partners are researching the expansion of an established preparation and induction support program for K-5 mathematics specialists into rural school systems.

Partner Organization(s): 
Award Number: 
0918223
Funding Period: 
Tue, 09/01/2009 to Wed, 08/31/2011
Project Evaluator: 
Horizon Research Inc.

Cyber-enabled Design Research to Enhance Teachers' Critical Thinking Using a Major Video Collection on Children's Mathematical Reasoning (Collaborative Research: Derry)

This project is demonstrating the use of cyber-enabled technologies to build and share adaptable interventions for pre- and in-service teacher growth that effectively make use of major video collections and have high promise of success at multiple sites. The cyber infrastructure being significantly extended through this project is supporting development and documentation of additional interventions for teacher professional development using this video collection, as well as other videos that might be added in the future.

Award Number: 
0822189
Funding Period: 
Mon, 09/15/2008 to Fri, 08/31/2012
Full Description: 

The Video Mosaic Collaborative features  videos of student mathematics reasoning,  tools and services to encourage learning, research and practices fostering the development of student reasoning.  The VMC is a collection and service portal intended to support three primary audiences—teacher educators and their pre-service and in-service students, practicing teachers, and researchers.  The Video Mosaic Collaborative features a 22-year longitudinal study of students’ mathematical reasoning skills as they are developed from elementary through high school grades.  The VMC has been carefully designed to leverage the insights and strategies that can be mined in this extensive and unique video collection featuring observations, interventions and interviews with students solving mathematics problems in the classroom and in informal learning settings.  A careful metadata strategy was designed by the library and education research partners in collaboration to capture elements for searching that include forms of reasoning and heuristics, math strand, math problem, NCTM standards, grade level and type of educational environment.  Students and researchers are identified and can be individually tracked through the collection.  Transcripts, student work and dissertations resulting from the videos are linked in metadata.  Tools, such as the VMCAnalytic, a video annotation and analysis tool, are provided to enable registered participants to reuse the videos for instruction, study and research by creating personal clips and combining clips to accomplish research goals such as demonstrating changes in reasoning for an individual student studying probability over several video sessions.  Unlike other video annotation tool, the VMC analytic creates  XML-based independent resources that can be kept private in the researcher’s workspace but that can also be shared.  Shared analytics will be mined for keywords, which will retrieve the video(s) being analyzed, thus adding user tagging to the metadata for the videos.  The analytic resources created are not independently searched and displayed but will display as part of the context for the videos in the collection, along with student work, dissertations, and ultimately published articles, etc., all of which form the critical context of research and study surrounding each video.

Different search strategies, guidance in using videos and opportunities to consult or collaborate with others will be provided for each primary audience of the VMC.  The latest iteration of the portal, with collections and services available for immediate use, will be presented and demonstrated at the DRK12 Principal Investigators’ meeting poster session.  Visitors to the poster will be encouraged to search the portal and to create a small analytic, in a hands-on, interactive one on one demonstration.  We believe that the VMC makes a unique and significant contribution to the efforts of teacher educators, practicing teachers and researchers to discover insights and develop innovative strategies to support the development of student reasoning in mathematics education.

Improving Teacher Preparation and Student Learning through Physics Education Research

This project develops resources to facilitate the involvement of college and university physics departments in the professional development of K-12 teachers of physics and physical science. Research investigates how students and teachers learn content and reasoning skills for applying concepts to real world situations; how teachers can learn content in a way that helps them promote student learning; and how teachers can learn to assess student understanding in a way that promotes student learning.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0733276
Funding Period: 
Sat, 09/15/2007 to Fri, 08/31/2012

Active Physics Teacher Community

This project augmenting the traditional professional development model with an online professional development platform—the Active Physics Teacher Community—that provides just-in-time support for teachers as they are enacting targeted units of the Active Physics curriculum. Teachers are helped in preparing lessons by providing them with formal instruction related to the lessons they are teaching in the classroom. In addition, teachers can participate in a moderated forum where they can share experiences.

Award Number: 
0733268
Funding Period: 
Sat, 09/15/2007 to Tue, 08/31/2010

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